Question

Find (f/g)(x). f(x)=/x^2-1 g(x)=/x-1

Answer 1

`((f)/(g))(x) = √(x + 1)`

Explanation:

Given

`f(x) = \sqrt{x^2 - 1`

`g(x) =\sqrt{x - 1`

Required

Find
`((f)/(g))(x)`

`((f)/(g))(x)` is calculated as:

`((f)/(g))(x) = (f(x))/(g(x))`

This gives:

`((f)/(g))(x) = (√(x^2 - 1))/(√(x - 1))`

Apply difference of two squares on the numerator

`((f)/(g))(x) = (√(x - 1)*√(x + 1))/(√(x - 1))`

`((f)/(g))(x) = √(x + 1)`